Krynicki, M. and M. Mostowski, Decidability problems in languages with Henkin quantifiers, Annals of Pure and Applied Logic 58 149–172.We consider the language L with all Henkin quantifiers Hn defined as follows: Hnx1…xny1…yn φ iff f1…fnx1. ..xn φ, ...,fn). We show that the theory of equality in L is undecidable. The proof of this result goes by interpretation of the word problem for semigroups.Henkin quantifiers are strictly related to the function quantifiers Fn defined as follows: Fnx1…xny1…yn φ iff fx1…xn (...) φ,...,f). In contrast with the first result we show that the theory of equality with all quantifiers Fn is decidable.We also consider decidability problems for other theories in languages L and L. (shrink)

We say that a semantical function is correlated with a syntactical function F iff for any structure A and any sentence we have A F A .It is proved that for a syntactical function F there is a semantical function correlated with F iff F preserves propositional connectives up to logical equivalence. For a semantical function there is a syntactical function F correlated with iff for any finitely axiomatizable class X the class –1X is also finitely axiomatizable (i.e. iff is (...) continuous in model class topology). (shrink)

Connections between partially ordered connectives and Henkin quantifiers are considered. It is proved that the logic with all partially ordered connectives and the logic with all Henkin quantifiers coincide. This implies that the hierarchy of partially ordered connectives is strongly hierarchical and gives several nondefinability results between some of them. It is also deduced that each Henkin quantifier can be defined by a quantifier of the form equation imagewhat is a strengthening of the Walkoe result. MSC: 03C80.

A fundamental notion in a large part of mathematics is the notion of equicardinality. The language with Hartig quantifier is, roughly speaking, a first-order language in which the notion of equicardinality is expressible. Thus this language, denoted by LI, is in some sense very natural and has in consequence special interest. Properties of LI are studied in many papers. In [BF, Chapter VI] there is a short survey of some known results about LI. We feel that a more extensive exposition (...) of these results is needed. The aim of this paper is to give an overview of the present knowledge about the language LI and list a selection of open problems concerning it. After the Introduction $(\S1)$ , in $\S\S2$ and 3 we give the fundamental results about LI. In $\S4$ the known model-theoretic properties are discussed. The next section is devoted to properties of mathematical theories in LI. In $\S6$ the spectra of sentences of LI are discussed, and $\S7$ is devoted to properties of LI which depend on set-theoretic assumptions. The paper finishes with a list of open problem and an extensive bibliography. The bibliography contains not only papers we refer to but also all papers known to us containing results about the language with Hartig quantifier. Contents. $\S1$ . Introduction. $\S2$ . Preliminaries. $\S3$ . Basic results. $\S4$ . Model-theoretic properties of $LI. \S5$ . Decidability of theories with $I. \S6$ . Spectra of LI- sentences. $\S7$ . Independence results. $\S8$ . What is not yet known about LI. Bibliography. (shrink)

We investigate theories of initial segments of the standard models for arithmetics. It is easy to see that if the ordering relation is definable in the standard model then the decidability results can be transferred from the infinite model into the finite models. On the contrary we show that the Σ₂—theory of multiplication is undecidable in finite models. We show that this result is optimal by proving that the Σ₁—theory of multiplication and order is decidable in finite models as well (...) as in the standard model. We show also that the exponentiation function is definable in finite models by a formula of arithmetic with multiplication and that one can define in finite models the arithmetic of addition and multiplication with the concatenation operation. We consider also the spectrum problem. We show that the spectrum of arithmetic with multiplication and arithmetic with exponentiation is strictly contained in the spectrum of arithmetic with addition and multiplication. (shrink)

Simple formula should contain only few quantifiers. In the paper the methods to estimate quantity and quality of quantifiers needed to express a sentence equivalent to given one.

The theorem to the effect that the languageL introduced in [2] is mutually interpretable with the first order language is proved. This yields several model-theoretical results concerningL.

A long-standing theme in discussion of perception and thought has been that our primary cognitive contact with individual objects and events in the world derives from our perceptual contact with them. When I look at a duck in front of me, I am not merely presented with the fact that there is at least one duck in the area, rather I seem to be presented withthisthing (as one might put it from my perspective) in front of me, which looks to (...) me to be a duck. Furthermore, such a perception would seem to put me in a position not merely to make the existential judgment that there is some duck or other present, but rather to make a singular, demonstrative judgment, that that is a duck. My grounds for an existential judgment in this case derives from my apprehension of the demonstrative thought and not vice versa. (shrink)

This book defends antitheodicism, arguing that theodicies, seeking to excuse God for evil and suffering in the world, fail to ethically acknowledge the victims of suffering. The authors argue for this view using literary and philosophical resources, commencing with Immanuel Kant's 1791 "Theodicy Essay" and its reading of the Book of Job. Three important twentieth century antitheodicist positions are explored, including "Jewish" post-Holocaust ethical antitheodicism, Wittgensteinian antitheodicism exemplified by D.Z. Phillips and pragmatist antitheodicism defended by William James. The authors argue (...) that these approaches to evil and suffering are fundamentally Kantian. Literary works such as Franz Kafka'sThe Trial, Samuel Beckett's Waiting for Godot, and George Orwell's Nineteen Eighty-Four, are examined in order to crucially advance the philosophical case for antitheodicism. (shrink)

Temporal Logic: From Ancient Ideas to Artificial Intelligence deals with the history of temporal logic as well as the crucial systematic questions within the field. The book studies the rich contributions from ancient and medieval philosophy up to the downfall of temporal logic in the Renaissance. The modern rediscovery of the subject, which is especially due to the work of A. N. Prior, is described, leading into a thorough discussion of the use of temporal logic in computer science and the (...) understanding of natural language. Temporal Logic: From Ancient Ideas to Artificial Intelligence thus interweaves linguistic, philosophical and computational aspects into an informative and inspiring whole. (shrink)

In his last book, David Armstrong sets out his metaphysical system in a set of concise and lively chapters each dealing with one aspect of the world. He begins with the assumption that all that exists is the physical world of space-time. On this foundation he constructs a coherent metaphysical scheme that gives plausible answers to many of the great problems of metaphysics. He gives accounts of properties, relations, and particulars; laws of nature; modality; abstract objects such as numbers; and (...) time and mind. (shrink)

Is consciousness a purely physical phenomenon? Most contemporary philosophers and theorists hold that it is, and take this to be supported by modern science. But a significant minority endorse non-physicalist theories such as dualism, idealism and panpsychism, among other reasons because it may seem impossible to fully explain consciousness, or capture what it's like to be in conscious states (such as seeing red, or being in pain), in physical terms. This Element will introduce the main non-physicalist theories of consciousness and (...) explain the most important arguments for them, and consider how they each respond to the scientific and other arguments in support of physicalism. This title is also available as Open Access on Cambridge Core. (shrink)

In this book Daniel Wegner offers a novel understanding of the relation of consciousness, the will, and our intentional and voluntary actions. Wegner claims that our experience and common sense view according to which we can influence our behavior roughly the way we experience that we do it is an illusion.

The ideal introduction for students of semantics, Lexical Meaning fills the gap left by more general semantics textbooks, providing the teacher and the student with insights into word meaning beyond the traditional overviews of lexical relations. The book explores the relationship between word meanings and syntax and semantics more generally. It provides a balanced overview of the main theoretical approaches, along with a lucid explanation of their relative strengths and weaknesses. After covering the main topics in lexical meaning, such as (...) polysemy and sense relations, the textbook surveys the types of meanings represented by different word classes. It explains abstract concepts in clear language, using a wide range of examples, and includes linguistic puzzles in each chapter to encourage the student to practise using the concepts. 'Adopt-a-Word' exercises give students the chance to research a particular word, building a portfolio of specialist work on a single word. (shrink)

The phenomenal powers view claims that phenomenal properties metaphysically necessitate their effects in virtue of how they feel, and thereby constitute non-Humean causal powers. For example, pain necessitates that subjects who experience it try to avoid it in virtue of feeling bad. I argue for this view based on the inconceivability of certain phenomenal properties necessitating different effects than their actual ones, their ability to predict their effects without induction, and their ability to explain their effects without appeal to laws (...) or regularities. I also offer a harmony argument according to which the view offers the best explanation for otherwise seemingly fortunate psychophysical regularities. I then outline the view’s main implications for the metaphysics of causation and philosophy of mind. (shrink)

This book integrates pragmatism and transcendental philosophy in examining the most serious problem defining the human condition, death and mortality. Its analysis of human limits and finitude is intended to be relevant to the concerns of philosophers specializing in, for example, transcendental philosophy, philosophical anthropology, pragmatism, Wittgenstein, and the philosophy of religion. Mortality is studied as providing a necessary framework within which questions concerning the meaningfulness or meaninglessness of human life become possible.

This book presents a collection of essays on institutional theory written by the German sociologist and Weber-expert M. Rainer Lepsius. Based on Weber's work, the author develops concepts of institutional theory, which he subsequently applies to topics such as National Socialism, democratization processes, German unification, and the institutionalization of the European Union. By showing how charismatic leadership can under certain circumstances threaten democratic structures and curtail individual freedoms, and by analyzing the structural and cultural conditions under which people develop trust (...) in political and social structures and ultimately come to support and comply with them, the author provides a sound analytical understanding of the development of democratic institutions and a democratic political culture. This collection of essays was edited, translated and commented on by Claus Wendt. (shrink)

The Ismaili Imam and Imamat -- Ethical foundations -- Tradition and modernity -- The ethos of modernism -- Pluralism and cosmopolitan ethics -- Cohesion within the Umma -- Islam and the West -- Cultivating and enabling environment -- Living the ethics of Islam -- Global convergence.

The socialist construction in Vietnam, aspect of human role.

A selection of important writings which together suggest that legal philosophy is the nerve of legal reasoning.

For over two centuries, Western scholars have discussed African philosophy and culture, often in disparaging, condescending terms, and always from an alien European perspective. Many Africans now share this perspective, having been trained in the western, empirical tradition. Makinde argues that, particularly in view of the costs and failings of western style culture, Africans must now mold their own modern culture by blending useful western practices with valuable indigenous African elements. Specifically, Makinde demonstrates the potential for the development of African (...) philosophy and even African traditional medicine. Following the lead of a number of countries with government policies of incorporating indigenous medicine with orthodox Western medicine, Makinde argues that traditional African practices should be taken seriously, both medically and scientifically. Further, he charges African scholars with the responsibility of investigating these and other elements of traditional African culture in order to dispel their mystery and secrecy through modern research and useful publications. (shrink)